Objective clustering protocol for single-molecule data: A lifetime vs. intensity study

Abstract

Single-molecule spectroscopy (SMS) is an exceptionally sensitive technique, but its inherently limited photon budget produces noisy data that can readily lead to subjective analyses, fitting errors, and reduced statistical power, obscuring true subpopulations and their dynamics. Here, we present an unbiased, objective method to cluster two-dimensional single-molecule data and demonstrate it on fluorescence lifetime--intensity correlations. The clustering method is based on Gaussian mixture modeling, with the optimal number of clusters determined through {information criteria (the Akaike and Bayesian information criteria and integrated completed likelihood) and supplemented by cluster quality metrics such as average cluster tightness and the fraction of points outside confidence ellipses, which guide the selection of statistically robust and physically meaningful clusters. The protocol was benchmarked on simulated datasets spanning clean, smeared, and noisy overlap-limited regimes, and applied to experimental data from Alexa Fluor 647 and QD 605. This approach reliably recovers relevant subpopulations even in the presence of noise and overlapping distributions, providing an objective framework for analyzing single-molecule heterogeneity, with limitations arising primarily under severe geometric overlap or extreme state-occupancy imbalance where distinct populations are no longer separable.